Solve for: {\text{begin}array l 2x+y=20 } 6x-5y=12\text{end}array .

Expression: $\left\{\begin{array} { l } 2x+y=20 \\ 6x-5y=12\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } y=20-2x \\ 6x-5y=12\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } y=20-2x \\ -5y=12-6x\end{array} \right.$

Divide both sides of the equation by $-5$

$\left\{\begin{array} { l } y=20-2x \\ y=-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 }x\end{array} \right.$

Since both expressions $20-2x$ and $-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 }x$ are equal to $y$, set them equal to each other forming an equation in $x$

$20-2x=-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 }x$

Solve the equation for $x$

$x=7$

Substitute the given value of $x$ into the equation $y=-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 }x$

$y=-\frac{ 12 }{ 5 }+\frac{ 6 }{ 5 } \times 7$

Solve the equation for $y$

$y=6$

The possible solution of the system is the ordered pair $\left( x, y\right)$

$\left( x, y\right)=\left( 7, 6\right)$

Check if the given ordered pair is the solution of the system of equations

$\left\{\begin{array} { l } 2 \times 7+6=20 \\ 6 \times 7-5 \times 6=12\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 20=20 \\ 12=12\end{array} \right.$

Since all of the equalities are true, the ordered pair is the solution of the system

$\left( x, y\right)=\left( 7, 6\right)$